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Minicourse: Fluid Dynamics. Prof. Monika Nitsche, with laboratory experiments by Peter Vorobieff. Fluid dynamics is a beautiful subject that builds on many areas of mathematics including vector analysis, mathematical modeling, complex variables, numerical analysis, and of course, differential equations. We will derive some of the basic equations of fluid dynamics. We will study simple analytical solutions, and simple numerical solutions using MATLAB (such as plotting streamlines, vorticity and pressure fields). This will be complemented by laboratory experiments in which the students are introduced to basic techniques such as measurements of lift and drag forces on a lifting surface and on a bluff body, as well as flow visualization using dye and smoke. Lift and drag on an airfoil and their dependence on the freestream velocity and the angle of attack will be related to ideal fluid flow theory using two-dimensional complex-variable representation of the flow. Vortex shedding behind a cylinder and a sphere visualized with dye and/or smoke injection will demonstrate transient flow patterns and the limitations of ideal flow theory. Professor Nitsche has been a faculty member in Applied Mathematics at UNM since 1999. Her research is in computational fluid dynamics, with emphasis on interfacial and vortex flows. Professor Nitsche is the Principal Investigator of the NSF-MCTP grant supporting the camp. Since 2008, she has organized UNMs participation in the SW Undergraduate Mathematics Research Conferences (SUnMaRC) series, which was held at UNM in 2009 and 2013. She has supported and mentored students in our department's Research for Undergraduate program. She also organizes and has cotaught the graduate student teacher training seminar and coordinates our department's Outreach Program. Professor Vorobieff is an experimental fluid dynamicists who has graciously offered to share his laboratory with you and illustrate some fluid dynamics with laboratory experiments. |
